## A new approach to the $$H_{\infty}$$ design of optimal digital linear filters.(English)Zbl 0678.93063

Summary: A novel approach to the solution of the $$H_{\infty}$$ estimation problem is developed. The solution is arrived at by embedding the problem within a fictitious mathematically equivalent $$\ell_ 2$$ framework in which a stable prefilter is introduced at the input of each noise source. The development is straightforward and relies on a polynomial system technique. Two numerical examples are presented to demonstrate the proposed approach.

### MSC:

 93E11 Filtering in stochastic control theory 93E10 Estimation and detection in stochastic control theory 46J15 Banach algebras of differentiable or analytic functions, $$H^p$$-spaces
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